What Is Place Value?
Place value is the idea that the value of a digit depends on its position in a number.
In the number 352:
- The 3 is in the hundreds place → it means 300
- The 5 is in the tens place → it means 50
- The 2 is in the ones place → it means 2
352 = 300 + 50 + 2. Same digits in different positions make completely different numbers: 352, 325, 253, 235, 532, 523 are all different.
The place value chart
| ... | Thousands | Hundreds | Tens | Ones | . | Tenths | Hundredths |
|---|---|---|---|---|---|---|---|
| 1,000 | 100 | 10 | 1 | 0.1 | 0.01 |
Each place is 10 times the place to its right. This is why our system is called base-10.
Why place value matters
Place value is the foundation of:
- Regrouping (carrying and borrowing): trading 10 ones for 1 ten
- Decimals: extending place value to the right of the decimal point
- Rounding: identifying which place to round to
- Expanded form: writing 352 as 300 + 50 + 2
- Multiplication: understanding why you "add a zero" when multiplying by 10
Related concepts
- How to Teach Place Value: full teaching guide
- Expanded form: breaking numbers into place value components
- Regrouping: the place value operation that makes addition/subtraction work